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FATIGUE life includes crack initiation life and crack propagation life. Fatigue crack propagation life has been modeled by many researchers.[1–5] Yet the modeling effort for predicting fatigue crack initiation is still in its early stage. It is critical to study the fatigue crack initiation life since this may be a substantial part of the component’s fatigue failure life as suggested by Liu and Choi.[5] During cyclic loading, persistent slip bands (PSB) are formed within the material due to the accumulation of dislocations impeded by immobile dislocations.[6,7] Chan et al.[8] observed that the average PSB width increases as the fatigue cycle increases. The PSB was proposed to reach a maximum width before cracking. Previous studies[9–14] assumed that the material would tend to form a crack instead of continuing to widen the PSB after a certain value due to minimization of Gibbs’-free energy change. However, this important assumption requires more experimental data to verify.

CHUN-YU OU is with the School of Industrial Engineering (Materials and Manufacturing Group), Purdue University, 315 Grant St., West Lafayette, IN 47906. Contact e-mail: [email protected] C. RICHARD LIU is with the School of Industrial Engineering (Materials and Manufacturing Group), Purdue University and also with the Birck Nanotechnology Center, Purdue University, 315 Grant St., West Lafayette, IN 47906 Manuscript submitted July 15, 2019.

METALLURGICAL AND MATERIALS TRANSACTIONS A

Maximum PSB width is one of the important factors in determining crack initiation life. Numerous TanakaMura type and micromechanical fatigue crack-initiation models[5,10–20] have utilized PSB as a coefficient for the life estimation. Lin et al.[15] proposed a fatigue crackinitiation model based on the accumulation of volume fraction of dislocations in PSB. Voothaluru and Liu,[12–14] and Fine and Bhat[11,16] predicted fatigue crack initiation life by obtaining an equation (Eq. [1]) by minimizing the Gibbs’-free energy change during the nucleation process. Here, tm is the maximum PSB width, Ni is the fatigue crack-initiation life, E is the Young’s modulus, cs is the surface energy, f is the energy efficiency coefficient, s=2is the resolved shear stress and cp =2 is the plastic slip per cycle. 

 ½1 Ni ¼ ðpEcs Þ pEftm ðDs=2Þ Dcp 2 Chan[18] developed a microstructure-based fatigue crack-initiation model that included PSB width as a factor for life prediction. Harvey et al.[19] presented a model for fatigue crack-initiation based on PSB width, PSB height displacement, and cumulative plastic strain. Liu and Choi[5] proposed a life estimation model for rolling contact fatigue with PSB width as an input. Previous crack-initiation models and the models reviewed by Man et al.[20] conjectured PSB width to be a constant of maximum value. Several experiments have investigated PSB width evolution.[20–23] However, there was no indication of the scope within which the maximum PSB is a constant. As a result, it is essential to study the characterized maximum PSB width to

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